The present disclosure is directed toward the measurement of electromagnetic properties of earth formations penetrated by a borehole. Measurements are made during the drilling operation or subsequent to the drilling operation. More particularly, the disclosure is directed toward the measure of resistivity or other electromagnetic properties by using one or more transmitters which induce an alternating voltage into the borehole and earth formation and by using multiple, longitudinally spaced receivers to detect the phase and amplitude of electromagnetic radiation induced within the borehole and formation. The receivers respond to different radial depths and therefore exhibit different "depths of investigation". Receiver responses are then combined to minimize the adverse effects of the borehole region and emphasize the response component from the formation thereby yielding a more accurate measure of the resistivity of the formation. Information related to variations in formation resistivity as a function of radial distance from the center of the borehole can also be extracted from the multiple receiver responses. The disclosure is even more particularly directed toward the elimination of the adverse effects of mutual coupling between multiple receivers, noting the receivers are coils subject to mutual coupling.
Induction techniques have been used for a number of years to determine the resistivity of earth formations penetrated by a borehole. Conceptually, an alternating current is applied to a transmitter of a borehole instrument thereby generating a primary electromagnetic field in earth formation in the vicinity of the transmitter. The primary field interacts with the earth formation thereby setting up a secondary field with amplitude and phase of this secondary field being related to the resistivity and other electromagnetic properties of the formation. Fluids in the borehole and the invasion of these borehole fluids into the formations can adversely effect the true resistivity measurement of virgin formation. Multiple receivers located at different longitudinal spacings from the transmitter are employed to measure the secondary field and minimize the effects of borehole and near borehole environs. The spacing between the transmitter and receiver determines to some extent the effective radial depth of the apparent formation resistivity measurement. The average radial depth of the resistivity measurements tends to increase as transmitter-receiver spacing increases if all other parameters are held constant. Therefore, the responses at receivers at two or more different longitudinal spacings can be combined to minimize the adverse effects of the borehole and near borehole environs on a true formation resistivity measurement.
Mutual coupling between pairs of receivers in multiple receiver resistivity devices can introduce error in formation resistivity measurements unless steps are taken to minimize these effects. The effects of mutual coupling are of increasing concern as more accurate and precise formation resistivity measurements are sought, especially in formations exhibiting high resistivity. The phenomena of mutual coupling will be described briefly by using as an example a borehole measuring system with an elongated downhole supportive body supporting a single transmitter and two longitudinally spaced receivers. The receivers are coils constructed so that the physical and electrical properties are as near the same as possible in practical application. The axes of the coils are parallel and are also parallel with the axis of the elongated downhole component of the system. On a common tubular body, the axes are also common or coincident. Primary and secondary fields induced within the formation and in the vicinity of the measuring instrument also induce voltages within the receivers. Voltage is the measured parameter at each receiver coil with the amplitude and phase of the voltage being related to resistivity of the formation at different depths of investigation. Each measured voltage also includes a component resulting from mutual coupling of the receiver pair. The transmitter induces an alternating current and corresponding voltage within the first receiver coil. Alternating current flowing within the first receiver coil also acts as a transmitter and induces a coupled current and associated voltage within the coil of the second receiver. This coupled voltage adds to the voltage induced by the secondary field generated within the formation. The total alternating current flowing within the coil of the second receiver likewise acts as a transmitter and likewise induces a coupled voltage component within the first receiver coil. Accurate formation resistivity measurements are predicated upon accurate measures of voltage induced within the earth formation and the elimination of, or compensation for, voltage components resulting from coupled receiver signals.
In prior measurement systems comprising one transmitter and two receivers, resistivity is computed from the ratio of receiver response in order to minimize borehole effects. V.sub.m,1 and V.sub.m,2 are defined as the measured voltages induced in receivers 1 and 2, respectively, where receiver 1 is at a shorter spacing with respect to the transmitter. Furthermore, V.sub.m,1 =V.sub.1 X.sub.1 S and V.sub.m,2 =V.sub.2 X.sub.2 S where V.sub.1 and V.sub.2 are unpreturbed voltages measured at receivers 1 and 2, respectively, X.sub.1 and X.sub.2 are terms which include the impedance associated with receivers 1 and 2, respectively, and S represents a term proportional to the power of the transmitter. The impedance portion of the terms X.sub.1 and X.sub.2 can vary as a function of temperature and other parameters. This variation is referred to as antenna drift. V.sub.1 and V.sub.2 are the desired parameters needed to compute accurate formation resistivities at the desired multiple depths of investigation. Defining R=V.sub.1,m /V.sub.2,m, one obtains log (R) =log (X.sub.1 /X.sub.2)+ log (V.sub.1 /V.sub.2) with the power term S canceling. By suspending the measuring device in air, remote from any conducting material, one obtains log(R.sub.air)=log((X.sub.1 /X.sub.2).sub.air)+log((V.sub.1 /V.sub.2).sub.air). If it is assumed that (X.sub.1 /X.sub.2)=(X.sub.1 /X.sub.2)air, then log(R)=log(R.sub.air)-log((V.sub.1 /V.sub.2).sub.air +log (V.sub.1 /V.sub.2)) or log(V.sub.1 /V.sub.2)=log (R)-log(R.sub.air)+log((V.sub.1 /V.sub.2).sub.air). Since R, and R.sub.air are measured quantities and (V.sub.1 /V.sub.2).sub.air can be computed, the ratio V.sub.1 /V.sub.2 can, in principle, be determined and the corresponding value of formation resistivity can be computed using techniques well known in the art. The assumption that (X.sub.1 /X.sub.2)=(X.sub.1 /X.sub.2)air does not, however, directly address errors due to temperature variations under operating conditions. Stated another way, the assumption that X.sub.1 /X.sub.2 is independent of temperature can introduce error in the final resistivity computation. To compensate for this source of error, the ratio (X.sub.1 /X.sub.2) is determined for each instrument as a function of temperature. Temperature within the borehole environment varies with depth resulting in a variation in X.sub.1 /X.sub.2 under operating conditions. In practice, therefore, the term X.sub.1 /X.sub.2 is not eliminated but rather corrected as a function of the operating temperature in the downhole environment. This technique requires that temperature corrections be made by using the predetermined relationship of X.sub.1 /X.sub.2 versus temperature along with an independent measurement of operating temperature. This method does not, however, correct the resulting formation resistivity values for errors resulting from mutual coupling between receivers. Although the mutual coupling term is relatively small when compared to other perturbations such as the contribution from the borehole, the mutual coupling term is significant in high accuracy and precision resistivity measurements, especially in highly resistive formations.
A second transmitter has been employed with the receiver pairs to further improve formation resistivity measurements by eliminating some of the previously discussed sources of error. More specifically, a longitudinal sequence of transmitter-receiver-receiver-transmitter on the support body has been employed with symmetrical spacing of all elements about a point midway between the two receivers. One technique involves the alternate measuring of voltage induced by one transmitter in the two receivers with the second transmitter being inactive or "OFF". This method also eliminates the previously discussed ratio of receiver impedance terms and, in addition, eliminates the previously discussed sources introduced by temperature variations since the necessity to make "air" readings is eliminated. Again, mutual coupling between receivers is not addressed introducing a source of error which is especially significant in measurements made in highly resistive formations.